$92$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $128$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 92}$ ${x = 4y-128}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-128}$ for $x$ in the first equation. ${(4y-128)}{+ y = 92}$ Simplify and solve for $y$ $ 4y-128 + y = 92 $ $ 5y-128 = 92 $ $ 5y = 220 $ $ y = \dfrac{220}{5} $ ${y = 44}$ Now that you know ${y = 44}$ , plug it back into ${x = 4y-128}$ to find $x$ ${x = 4}{(44)}{ - 128}$ $x = 176 - 128$ ${x = 48}$ You can also plug ${y = 44}$ into ${x+y = 92}$ and get the same answer for $x$ ${x + }{(44)}{= 92}$ ${x = 48}$ There were $48$ home team fans and $44$ away team fans.